Robust optimization methods for cardiac sparing in tangential breast IMRT

2015 ◽  
Vol 42 (5) ◽  
pp. 2212-2222 ◽  
Author(s):  
Houra Mahmoudzadeh ◽  
Jenny Lee ◽  
Timothy C. Y. Chan ◽  
Thomas G. Purdie
Keyword(s):  
Robust Optimization ◽  
Optimization Methods ◽  
Breast Imrt ◽  
Cardiac Sparing

scholarly journals Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4642
Author(s):  
Li Dai ◽  
Dahai You ◽  
Xianggen Yin
Keyword(s):  
Robust Optimization ◽  
Dirichlet Process ◽  
Forecast Error ◽  
Optimization Methods ◽  
Optimization Method ◽  
Gaussian Mixture ◽  
Data Driven ◽  
Uncertainty Sets ◽  
Uncertainty Set ◽  
Simulation Results

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

The Effect of Different Optimization Methods on Robustness for Robust Optimization Design

2014 ◽  
Vol 721 ◽  
pp. 464-467
Author(s):  
Tao Fu ◽  
Qin Zhong Gong ◽  
Da Zhen Wang
Keyword(s):  
Robust Optimization ◽  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Parameters ◽  
Hybrid Particle Swarm Optimization ◽  
Design Variables ◽  
Robust Optimization Design

In view of robustness of objective function and constraints in robust design, the method of maximum variation analysis is adopted to improve the robust design. In this method, firstly, we analyses the effect of uncertain factors in design variables and design parameters on the objective function and constraints, then calculate maximum variations of objective function and constraints. A two-level optimum mathematical model is constructed by adding the maximum variations to the original constraints. Different solving methods are used to solve the model to study the influence to robustness. As a demonstration, we apply our robust optimization method to an engineering example, the design of a machine tool spindle. The results show that, compared with other methods, this method of HPSO(hybrid particle swarm optimization) algorithm is superior on solving efficiency and solving results, and the constraint robustness and the objective robustness completely satisfy the requirement, revealing that excellent solving method can improve robustness.

Applied Technology in Robust Optimization Model for Airport Flow Allocation

2013 ◽  
Vol 859 ◽  
pp. 463-467
Author(s):  
Shang Wen Yang ◽  
Yong Jie Yan
Keyword(s):  
Robust Optimization ◽  
Real World ◽  
Optimization Model ◽  
Numerical Test ◽  
Negative Relationship ◽  
Optimization Methods ◽  
Test Results ◽  
Airport Capacity ◽  
Applied Technology ◽  
Typical Model

To solve the airport arrival and departure flow allocation problem under the condition of uncertain capacity, one of robust optimization methods was applied. Applied technology in Robust Optimization Model with the aim to minimize expected delayed flights at certain robustness level was proposed. The robustness factor constraint, airport capacity curve constraint, fix capacity constraint and airport capacity scenario constraint were included. To test how well the model would be in real world, a numerical test was performed based on the data of a Chinese international airport. Test results show that there is a negative relationship between expected delay flights and robustness level. Compared with typical model, Applied Technology in Robust Optimization Model proposed achieves better effect at the same robustness level.

scholarly journals HyAdamC: A New Adam-Based Hybrid Optimization Algorithm for Convolution Neural Networks

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4054
Author(s):  
Kyung-Soo Kim ◽  
Yong-Suk Choi
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Robust Optimization ◽  
Image Classification ◽  
Large Scale ◽  
Optimization Methods ◽  
Optimization Method ◽  
Hybrid Optimization ◽  
Computation Method ◽  
Convolution Neural Networks

As the performance of devices that conduct large-scale computations has been rapidly improved, various deep learning models have been successfully utilized in various applications. Particularly, convolution neural networks (CNN) have shown remarkable performance in image processing tasks such as image classification and segmentation. Accordingly, more stable and robust optimization methods are required to effectively train them. However, the traditional optimizers used in deep learning still have unsatisfactory training performance for the models with many layers and weights. Accordingly, in this paper, we propose a new Adam-based hybrid optimization method called HyAdamC for training CNNs effectively. HyAdamC uses three new velocity control functions to adjust its search strength carefully in term of initial, short, and long-term velocities. Moreover, HyAdamC utilizes an adaptive coefficient computation method to prevent that a search direction determined by the first momentum is distorted by any outlier gradients. Then, these are combined into one hybrid method. In our experiments, HyAdamC showed not only notable test accuracies but also significantly stable and robust optimization abilities when training various CNN models. Furthermore, we also found that HyAdamC could be applied into not only image classification and image segmentation tasks.

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